Question

mean of 20 values is X, 21 values is 45 average increased by 1 what what is the average​

Answer 1

Answer:

Average (20 values) = 24

Average (21 values) = 25

Step-by-step explanation:

We can solve it in two ways,

Method 1

We have,

Mean of 20 values = x

21st value = 45

After considering the 21st value, the average is increased by 1.

Now,

Mean = Sum of values/Total no. of values

Let the sum of values be S.

x = S/20

Again when 21st value is included,

Mean = (S + 45)/21

Now, according to the Question,

Mean of 21 values = Mean of 20 values + 1

(S + 45)/21 = (S/20) + 1

(S + 45)/21 = (S/20) + (20/20)

(S + 45)/21 = (S + 20)/20

Cross multiplying we get

20(S + 45) = 21(S + 20)

20S + 900 = 21S + 420

21S - 20S = 900 - 420

S = 480

Hence,

Sum of 20 values = 480

Now,

Average of 20 values = 480/20

= 24

Also,

Average of 21 values = (480 + 45)/21

= 525/21

= 25

Hence,

Average (20 values) x = 24

Average (21 values) = 25

Method 2

We have,

Mean of 20 values = x

21st value = 45

After considering the 21st value, the average is increased by 1.

Now,

Mean = Sum of values/Total no. of values

Let the sum of values be S.

x = S/20

S = 20x

Again when 21st value is included,

Mean = (S + 45)/21

= (20x + 45)/21

Now, according to the Question,

Mean of 21 values = Mean of 20 values + 1

(20x + 45)/21 = x + 1

(20x + 45)= 21(x + 1)

20x + 45 = 21x + 21

21x - 20x = 45 - 21

x = 24

Hence,

Average (20 values) x = 24

Average (21 values) = 25

Hope it helped